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Math Help - Distance of x

  1. #1
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    Distance of x

    Can anyone help me solve this?

    a maan can cycle from his house to a railway station and back in a certain time at 12km/h. if he rides out at 8km/h and returns by motor at 15km/h, he takes 15mins longer on the double journey? Find the distance between his house and the station.

    I'm not really sure how to approach this problem. Whether to name the distance x, or use the distance/time formula.

    please help
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  2. #2
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    Hello bloo.tomarto
    Quote Originally Posted by bloo.tomarto View Post
    Can anyone help me solve this?

    a maan can cycle from his house to a railway station and back in a certain time at 12km/h. if he rides out at 8km/h and returns by motor at 15km/h, he takes 15mins longer on the double journey? Find the distance between his house and the station.

    I'm not really sure how to approach this problem. Whether to name the distance x, or use the distance/time formula.

    please help
    I think you need to do both of the things you've suggested.

    Let the distance between his house and the station be x km. Then, using the formula:
    \text{time} = \frac{\text{distance}}{\text{speed}}
    • the time he takes to cycle one way is \frac{x}{12} hours.


    • the time he takes to ride one way is \frac{x}{8} hours.


    • the time he takes to motor one way is \frac{x}{15} hours.

    Finally, the time to ride + time to motor = 2 x time to cycle one way +\tfrac14 hour. So we get:
    \frac{x}{8}+\frac{x}{15}= 2\times\frac{x}{12}+\frac14
    Can you complete it now? (Hint: Begin by multiplying both sides by 120 \;(=8\times15) to get rid of fractions.)

    (I make the distance between his house and the station 10 km.)

    Grandad
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